Exponents and Logarithms

Simply Exponential

100

Writing using the nth root.

4^2.5

sqrt(4⁵)

200

a^-3

Written with positive exponents

1/a³

300

(6^1/3)²

Written as an nth root. 

cube root(36) or cube root(6²)

400

3x^-4

Written with positive exponents 

3/x⁴

500

(x^-3y²z⁴)/(y³z^-1)

Simplified

z⁵/x³y

What's up?

100

3^x=81

x=4

200

5^3x=125²

x=3/4

300

27^x=9^x-2

x=-4

400

(y^5x)²=y^-5

x=-1/2

500

1/36=6^x+2

x=-4

The ol'switch-a-roo

100

7^x=14

In logarithmic form

log₇14=x

200

log₄25=y

In exponential form

4^y=25

300

2⁽⁵⁾=x+1

In logarithmic form

log₂(x+1)=5

400

ln7=x

In exponential form

e^x=7

500

e^x=12

In logarithmic form

Ln12=x

#fake

100

log₂2

1

200

log_ex

lnx

300

log₅5³

3

400

log_x1

0

500

log_-108

Undefined

Rand-o Land-o

100

Evaluate log₅21

approx. 1.892

200

Condense.

log (5)+1

log50

300

if ln(x)= 3  and    ln(y)=21

What is log₃21

7

400

Expand.

ln[(x²y^1/2)/x]

2lnx+1/2lny-lnx

500

Simplify.

lne⁶-lne²+lne

5